Asymptotic properties of conditional quantiles of the Cauchy distribution in Hilbert space |
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Authors: | S. Ya. Shatskikh |
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Affiliation: | (1) Samara State University, Samara, Russia |
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Abstract: | In this paper, we consider the conditional distributions that are induced by finite-dimensional projections of a σ-additive Cauchy measure defined in a real Hilbert space. In the case where the dimension of projections tends to infinity, we establish the almost sure convergence of “conforming” sequences of finite-dimensional conditional quantiles and prove the strong law of large numbers for the triangular array scheme applied to a family of conditional distributions. Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997, Part III. |
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